In cutting a workpiece on a machine tool such as a machining center, a cutting simulation performed to simulate changes in the shape of the workpiece on a computer is required to efficiently process the changes in the shape of the workpiece and display consecutive changes in the shape of the workpiece at high speeds on a screen. In general, the cut surface created by cutting operations may have a complicated shape that is defined by the relative motion between the cutting tool and the workpiece. Therefore, the workpiece shape is often represented, for example, in a voxel model or a dexel model that employs a set of so-called cells or minute cubes or prisms.
By way of example, a method for performing high-speed simulations using the voxel or dexel model is disclosed in Patent Document 1. The method uses the shape data that is obtained by converting the three-dimensional workpiece model into a dexel model. Then, the method calculates a sweep shape formed when the tool moves along a travel path and calculates the wedged and cylindrical shapes that constitute the sweep shape. Then, the respective bottom surfaces are turned into a polygon to remove a hidden surface using three-dimensional graphics hardware capable of depth buffering, thereby creating an intermediate image. At this time, the upper edge of a dexel is cut off on the basis of a depth value stored in the depth buffer. The upper end portion of the dexel is then turned into a polygon, whose hidden surface is in turn eliminated using the three-dimensional graphics hardware, thereby creating a final image for display on a screen.